There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Using Multivariate Statistics

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

Linear Matrix Inequalities in System and Control Theory

A femtosecond hybrid mode locked Rhodamine B dye laser

Summary There has been very little literature on the mid seasonspatial variability of fruit production in horticulturecrops published to date. Most of the existing literaturerefers to data collected post harvest. Crop load datataken prior to hand thinning and prior to harvest werecollected in 3 blocks of a commercial apple ( Malus do-mestica Borkh.) orchard in the province of Ferrara, It-aly. The purpose of the survey was to characterize thewithin field variability of crop load, using spatial sta-tistics, and assess the effectiveness of the hand-thin-ning treatment. Crop load estimations were taken at156 sites pre and post hand-thinning over a defineddistance (0.8 m) and the data used to model a vario-gram and associated spatial variation. Variation in thespatial distribution of the fruit load prior to thehand-thinning was observed, indicating a possibility tospatially differentially manage the orchard. No spatialvariation in fruit number wa s observed prior to harvest(post-thinning), indicating that thinning had removedthe previously observed spatial variation in crop load.Under the current uniform management approach thisindicates that thinning has been effectively imple-mented. However, the spatial variation observed priorto thinning may indicate that a differential crop loadmanagement strategy may be optimal for maximizingquality in the orchard.

https://www.pubhort.org/ejhs/2009/file_968077.pdf

Spatial Analysis of the Effect of Fruit Thinning on Apple Crop Load

Supercontinua spanning 320 -2400 nm have been generated in long photonic-crystal- fiber tapers. Total average powers of over 3.5 W and spectral-power-densities in the blue of over 5 mW/nm are demonstrated. Use as a broadly-tunable pulse source is proposed.

Multi-watt supercontinuum generation from 0.3 to 2.4 μm in PCF tapers

The first passive mode locking of the continuous wave (cw) DCM dye laser is reported. Subpicosecond pulses as short as 0.68 ps were obtained over the spectral region from 655 to 673 nm from a simple linear cavity with no dispersion optimisation. The dye 1,3′ Diethyl 4,2′ quinolythiacarbocyanine iodide (DQTCI) was used as the saturable absorber.

Passive Mode Locking of the Continuous Wave DCM Dye Laser

The robust control problem for nonlinear sys-tems is discussed from the standpoint of the amplitudesensitivity of the nonlinear plant and ﬁnal control system.Failure to recognize and accommodate this factor may giverise to nonlinear control systems that behave diﬀerently forsmall versus large input excitation, or perhaps exhibit limitcycles or instability. Sinusoidal-input describing functions(sidfs) are shown to be eﬀective in dealing with amplitudesensitivity in two areas: modeling (providing plant mod-els that achieve an excellent trade-oﬀ between conservatismand robustness) and nonlinear control synthesis. In ad-dition, sidf-based modeling and synthesis approaches arebroadly applicable. Several practical SIDF-based nonlinearcompensator synthesis approaches are presented and illus-trated via application to a position control problem.Keywords: Nonlinear control systems; describingfunctions; frequency-domain modeling; fourier analysis;frequency-domain design; robust control; synthesis meth-ods; pid control; fuzzy logic; position control.

James Taylor

Papers

A femtosecond hybrid mode locked Rhodamine B dye laser

Spatial Analysis of the Effect of Fruit Thinning on Apple Crop Load

Multi-watt supercontinuum generation from 0.3 to 2.4 μm in PCF tapers

Passive Mode Locking of the Continuous Wave DCM Dye Laser

Robust nonlinear control based on describing function methods